Method and apparatus for actuation of a two-axis MEMS device using three actuation elements

ABSTRACT

Apparatus and methods are provided for driving a two-axis MEMS mirror using three non-contact actuation elements or electrodes. A differential bi-directional mirror control uses unipolar drive voltages biased at a suitable value. Transformation functions map two-axis tip-tilt commands to three actuation drive signals for selected electrode orientations and sizes.

CROSS-REFERENCES TO RELATED APPLICATIONS

[0001] NOT APPLICABLE

STATEMENT AS TO RIGHTS TO INVENTIONS MADE UNDER FEDERALLY SPONSOREDRESEARCH OR DEVELOPMENT

[0002] NOT APPLICABLE

REFERENCE TO A “SEQUENCE LISTING,” A TABLE, OR A COMPUTER PROGRAMLISTING APPENDIX SUBMITTED ON A COMPACT DISK.

[0003] NOT APPLICABLE

BACKGROUND OF THE INVENTION

[0004] The invention relates to actuation of a micro-electromechanicalsystem (MEMS) device, and in particular to actuation of a two-axistip-tilt MEMS mirror. The invention finds application toelectrostatically actuated optical switching, but it is not so limited.

[0005] Schemes for electrostatic and magnetic actuation of two-axistip-tilt MEMS mirrors using four actuation elements are well known. Afour element configuration has the advantage of straight-forwardsymmetry with respect to orthogonal tip-tilt axes, so that thetransformation function between tilt orientation and applied voltage orcurrent at each actuation element is relatively straight-forward. Thegeneral method of actuation using four electrodes is to actuateelectrodes in pairs on a common side of an axis to tilt about the axis.

[0006] In order to control the individual actuation elements, eachelement requires its own voltage or current supply-line and associateddrive circuitry. In the case of an optical switch using arrays ofclosely spaced mirrors, the large number of lines and drivers becomes alimiting factor in system design. Due to packing constraints, routing ofthe lines becomes challenging as the number of MEMS devices in the arrayis increased. Furthermore, the system cost scales as the number ofdrivers is increased due the larger number of electronic components.What is needed is a scheme to reduce the number of drivers and lines toreduce both the interconnect and driver problems.

SUMMARY OF THE INVENTION

[0007] According to the invention, a method and apparatus are providedfor driving a two-axis MEMS mirror using three non-contact actuationelements or electrodes. A differential bi-directional mirror controluses three actuation drive signals biased at a suitable value.Transformation functions map two-axis tip-tilt commands to threeactuation drive signals for selected electrode orientations and sizes.

[0008] The theoretical basis as presented here for using threeelectrodes in an electrostatic drive is applicable to other casesinvolving two-axis tip-tilt devices, including electromagnetic actuatorsfor MEMS devices. Therefore, the disclosure is to be understood toaddress the case of using three electrodes to drive a two-axis tip-tiltdevice.

[0009] The invention will be better understood by reference to thefollowing detailed description in connection with the accompanyingembodiments.

BRIEF DESCRIPTION OF THE DRAWINGS

[0010]FIG. 1 is a perspective view in partial cutaway illustratingrelative positioning of an array of two-axis MEMS mirrors and threedrive electrodes according to the invention.

[0011]FIG. 2 is a top view of a two-axis MEMS mirror and three driveelectrodes in which hinge axes are directly aligned to the electrodesaccording to the invention.

[0012]FIG. 3 is a top view of a two-axis MEMS mirror and three driveelectrodes in which hinge axes are randomly aligned to the electrodesaccording to the invention.

DETAILED DESCRIPTION OF THE INVENTION

[0013] Referring to FIG. 1 and FIG. 2, there is shown an example of aMEMS mirror 4 in an array 10 driven by three equivalent actuationelements 1, 2, and 3. In the case of the double-gimbaled mirror shown,outer hinges 5 and 6 allow the outer ring and mirror to rotate about they-axis, and inner hinges 7 and 8 allow the mirror 4 to rotate about thex-axis, where both x and y axes are in the plane of the mirror 4. Forthis particular embodiment of the invention, the x-axis of rotation isaligned to the gap 9 between elements 1 and 2 and points in thedirection of element 3. In another embodiment of the invention, shown inFIG. 3, the relative orientation of the drive elements to the hinge axesis rotated by an arbitrary angle. In all embodiments of the invention,the forces that actuate the tilt of the mirror are provided by the threeactuation elements 1, 2 and 3. The forces may be derived by variousmeans including electrostatic and magnetic means. In the electrostaticcase, the elements 1, 2, 3 may be flat metallic electrodes. By applyinga voltage to each electrode, an electrostatic force is created betweenthe electrode and an electrically conductive layer (not shown) in themirror 4 (including the mirror surface itself), causing the mirror 4 totilt through a controlled angle as hereinafter explained. In themagnetic case, the elements 1, 2, 3 may be planar circular coils ofconductive traces. By applying a current from a current source to eachof the coils, magnetic fields thus created interact with a ferromagneticregion (not shown) in the mirror 4 (including the mirror materialitself), an interacting magnetic force is induced, causing the mirror 4to tilt.

[0014] The actuation elements need not be of equal area, or need theyproduce an equivalent amount of force for an equal drive signal. Thus,an alternative embodiment of the invention within the scope of theclaims is one in which at least one of the three actuation elements isdifferent in a significant parameter than the other two. They can differin a variety of ways including, but not limited to, area, shape, andthickness.

[0015] A central aspect of the invention is the method by which the tiltof the mirror is controlled using three actuation elements. Since thereare two independent rotation axes, two independent command signals arerequired. These command signals are defined to be V_(x) and V_(y) forcontrol of rotation about the x-axis and y-axis, respectively. Key tothe problem is determining how to map the command signals uniquely intothe three drive signals, which are denoted as V₁, V₂ and V₃. Thesesignals may be generated by selected voltage sources or current sourcedepending on the type of actuation mechanism. The mapping can begenerally represented by the following system of liner equations:

V ₁ =AV _(x) +BV _(y) +V _(f1),

V₂ =CV _(x) +DV _(y) +V _(f2), and

V ₃ =EV _(x) +FV _(y) +V _(f3),

[0016] where A, B, C, D, E, F, V_(f1), V_(f2), and V_(f3) are allconstants independent of V_(x) and V_(y). Any number of mapping methodscould be employed. However, not all methods produce the same controlcharacteristics. Therefore, the problem is constrained so that thefollowing properties are maintained by the mapping:

[0017] ( 1) The command signal V_(x) is coupled to effect displacementof the MEMS device only about the x-axes.

[0018] (2) The command signal V_(y) is coupled to effect displacement ofthe MEMS device only about the y-axes.

[0019] (3) The command signal V_(x) is differential so that no change inthe average drive signal to the three elements occurs.

[0020] (4) The command signal V_(y) is differential so that no change inthe average drive signal to the three elements occurs.

[0021] Constraints (1) and (2) ensure that there is no or littlecross-talk between the two independent rotation directions. Constraints(3) and (4) linearize the response of the system to the command signalsV_(x) and V_(y). Both these properties, greatly simplify the feedbackcircuitry or algorithm needed in closed-loop operation of the mirrors.

[0022] By applying the constraints (1)-(4), the relative relationshipsbetween the constants A, B, C, D, and E are necessarily constrained,that is, they cannot assume arbitrary values. Their values also dependon the particular configuration of the actuation elements and on therelative orientation of the tilt axes to the actuation elements. For theembodiment depicted in FIG. 1 and FIG. 2, where the three elements areall equivalent and oriented as shown, for constraint (1) to be alwaystrue, it is necessary that the sum of A and C be linearly proportionalto E. For constraint (2) to be true, it is necessary that B equal D.Constraint (3) implies that the sum of A, C and D equal zero, andconstraint (4) implies that the sum of B, D and E equal zero. All ofthese conditions must be true simultaneously. For this to occur, F mustbe equal to −2B, C must be equal be to −A, and E must be equal to zero.Thus, the set of general equations for the mapping are reduced to thefollowing set of equations, which is denoted as M₁:

V ₁ =AV _(x)−(F/2)V _(y) +V _(f1),

V ₂ =−AV _(x)−(F/2)V _(y) +V _(f2), and

V ₃ =FV _(y) +V _(f3).

[0023] The set of equations M₁ define how the two-axis command signalsare mapped into the three drive signals. The bias values V_(f1), V_(f2),and V_(f3) may be all equal in value, or one or more may be differentfrom the others. The M₁ mapping applies to the case where the threeactuation elements are all equivalent in shape and form, are equallyspaced apart, and are oriented with respect to the tilt axes as shown inFIG. 2. It is understood that the M₁ mapping is unique to the elementlabeling system shown in FIG. 1 and FIG. 2 and to the choice of axesorientation shown in these figures. There are several permutations ofelement labeling and axes orientation for which this mapping applies butwith trivial changes in assignment of the drive signals V₁, V₂, and V₃and in the sign of the coefficients A and F.

[0024] The M₁ mapping described above applies only if the orientation ofthe actuation elements relative to the hinges is consistent with that inFIG. 2. In a generalized case, the orientation of the drive elementsneed not conform to that pictured in FIG. 2. The elements can be rotatedwith respect to the directions defined by the mirror hinge axes. Anarbitrary orientation of the elements is depicted in FIG. 3, where therotation angle θ is defined as a counter-clockwise rotation of theelements from the orientation shown in FIG. 2. In order to maintain thevalidity of constraints (1)-(4) despite the relative orientation of thedrive elements, the mapping of the command signals to the drive signalsmust be modified. This is performed by applying a change of coordinatesystem in which the new axes are rotated by an angle θ with respect tothe original axes. The resulting new mapping is described by thefollowing new set of linear equations, which is denoted as M₃:$\begin{matrix}{{V_{1} = {{\left( {{{ACos}(\theta)} + {\left( {F/2} \right){{Sin}(\theta)}}} \right)V_{x}} + {\left( {{{ASin}(\theta)} - {\left( {F/2} \right){{Cos}(\theta)}}} \right)V_{y}} + V_{f1}}},} \\{{V_{2} = {{\left( {{- {{ACos}(\theta)}} + {\left( {F/2} \right){{Sin}(\theta)}}} \right)V_{x}} + {\left( {{- {{ASin}(\theta)}} - {\left( {F/2} \right){{Cos}(\theta)}}} \right)V_{y}} + V_{f2}}},{and}} \\{V_{3} = {{{- F}\quad {{Sin}(\theta)}V_{x}} + {F\quad {{Cos}(\theta)}V_{x}} + {V_{f3}.}}}\end{matrix}$

[0025] The mapping described by these equations is the general formwhere the electrodes are of equal size in connection with control of thedouble-gimbaled mirror 4 by the three drive elements 1, 2, and 3. Thebias values V_(f1), V_(f2), and V_(f3) may be all equal or one or moremay be different from the others.

[0026] A more specific embodiment of the invention provides asimplification to the mapping. A desirable, but not necessary, propertyof the mapping is that it be invariant to a rotation of the driveelements by an integral multiple of 120 degrees. From the symmetry ofthe three elements, if the drive elements are rotated by an integralmultiple of 120 degrees with respect to the mirror hinges, the newconfiguration is completely equivalent to the unrotated configurationexcept for an inconsequential change in the labeling of the elements.For the mapping to remain unchanged, except for an inconsequentialpermutation of the labels 1, 2 and 3, then the ratio of the constant Ato the constant F must be constrained to equal to {square root}{squareroot over (3/2)}. Thus one specific type of mapping contemplated by thisinvention is described by the following set of linear equations, whichis denoted as M₄: $\begin{matrix}{{V_{1} = {{{F\left( {{\left( {\sqrt{3}/2} \right){{Cos}(\theta)}} + {\left( {1/2} \right){{Sin}(\theta)}}} \right)}V_{x}} + {{F\left( {{\left( {\sqrt{3}/2} \right){{Sin}(\theta)}} - {\left( {1/2} \right){{Cos}(\theta)}}} \right)}V_{y}} + V_{f}}},} \\{{V_{2} = {{{F\left( {{{- \left( {\sqrt{3}/2} \right)}{{Cos}(\theta)}} + {\left( {1/2} \right){{Sin}(\theta)}}} \right)}V_{x}} + {{F\left( {{{- \left( {\sqrt{3}/2} \right)}{{Sin}(\theta)}} - {\left( {1/2} \right){{Cos}(\theta)}}} \right)}V_{y}} + V_{f}}},{and}} \\{V_{3} = {{{- F}\quad {{Sin}(\theta)}V_{x}} + {F\quad {{Cos}(\theta)}V_{x}} + {V_{f}.}}}\end{matrix}$

[0027] It is this unique mapping for which constraints (1)-(4) aremaintained in addition to being invariant to a rotation of the driveelements by an integral multiple of 120 degrees. Mapping M₄ only appliesto the case where the drive elements are all equivalent and equallyspaced as depicted in FIG. 3.

[0028] The invention has been explained with reference to specificembodiments. Other embodiments will be evident to those of ordinaryskill in the art. For example, the invention is not specific to adouble-gimbaled mirror. A different relative orientation of the mirroraxes and three electrodes from what was described is permissible, whichresults in different coefficients in the mapping between the twodifferential commands and the three electrode commands. It is thereforenot intended that this invention be limited, except as indicated by theappended claims.

What is claimed is:
 1. An apparatus with two axes of controllablebi-directional angular displacement comprising: a platform susceptibleof reorientation around the two axes in response to actuation; first,second, and third actuation elements located in proximity to theplatform to provide noncontact actuation to the platform; three controlsources operative to provide independent control forces to the first,second and third actuation elements; and control means for mappingselected positions relative to the two axes of angular displacement tothe three control forces.
 2. The apparatus according to claim 1 whereinthe actuation elements are electrodes and the control sources comprisevoltage sources.
 3. The apparatus according to claim 1 wherein theactuation elements are electromagnetic elements, the plate includes aferromagnetic region, and the control sources comprise current sources.4. The apparatus according to claim 1 wherein the control means isoperative to map according to the following relation: [V ₁ , V ₂ , V ₃]=[M ₁ ][V _(x) , V _(y)] where the actuation elements are ofsubstantially equal area and are symmetrically disposed with respect toa first one of the axes.
 5. The apparatus according to claim 4 whereinthe first actuation element is disposed in direct alignment with thefirst one of the axes and wherein the second actuation element and thethird actuation element are each disposed symmetrically on opposingsides of the first one of the axes.
 6. The apparatus according to claim1 wherein two of the actuation elements are of unequal area relative toa first one of the actuation elements.
 7. The apparatus according toclaim 1 wherein the first one of said actuation elements is disposed indirect alignment with a first one of the axes and the second actuationelement and the third actuation elements are each disposed symmetricallyon opposing sides of the first one of the axes.
 8. The apparatusaccording to claim 1 wherein the control means is operative to mapaccording to the following relation: [V ₁ , V ₂ , V ₃]=[M₃ ][V _(x) , V_(y)] wherein said actuation elements are of equal area and are disposedin random alignment with respect to the two axes.
 9. The apparatusaccording to claim 1 wherein the control means is operative to mapaccording to the following relation: [V ₁ , V ₂ , V ₃ ]=[M ₄ ][V _(x) ,V _(y)] wherein said actuation elements are of equal area and mapping isinvariant to rotation of said actuation elements around a central z axisby multiples of 120 degrees.
 10. The apparatus according to claim 1wherein the actuation elements are of unequal area and are disposed inrandom alignment with respect to the axes.
 11. The apparatus accordingto claim 1 wherein the platform is further susceptible of displacementalong a z axis substantially normal to the platform.
 12. A method forlinearized control of an apparatus with two axes of controllablebi-directional angular displacement, the apparatus having a platformsusceptible of reorientation around the two axes in response toactuation, three actuation elements located in proximity to the platformto provide noncontact actuation to the platform, three control sourcesoperative to provide independent control forces to the three actuationelements, and control means for mapping selected positions relative tothe two axes of angular displacement to the three control forces, themethod comprising the steps of: selecting an angle of displacement ofthe platform; mapping the angle of displacement to angle commands fordisplacement around an x axis and a y axis; mapping the two anglecommands according a specified mapping matrix from first and secondcontrollable angles to three bias voltages for producing angle-inducingelectrode voltage commands for use to control the first and secondcontrollable angles; and applying said angle-inducing electrode voltagecommands to said three control sources to vary axial displacement of theactuation elements over said first and second controllable angles. 13.Method for linearized control of an apparatus with two axes ofcontrollable bi-directional angular displacement, the apparatus having aplatform susceptible of reorientation around the two axes in response toactuation, three actuation elements located in proximity to the platformto provide noncontact actuation to the platform, three control sourcesoperative to provide independent control forces to the three actuationelements, and control means for mapping selected positions relative tothe two axes of angular displacement to the three control forces, themethod comprising the steps of: selecting an angle of displacement ofthe platform; mapping the angle of displacement to angle commands fordisplacement around an x axis and a y axis; mapping the two anglecommands according a specified mapping matrix from first and secondcontrollable angles to three bias currents for producing angle-inducingelectrode current commands for use to control the first and secondcontrollable angles; and applying said angle-inducing electrode currentcommands to said three control sources to vary axial displacement of theactuation elements over said first and second controllable angles.